Macbook Pro - how to copy data off hard disk

[Snatch1]

2013 Macbook Pro is dead (son spilled a glass of water over the keyboard). I need to copy the data of the hard disk before sending it off to be repaired/replaced by insurance company (back up failed, user set up error!)

I have a USB to SATA 3.0 adapter. Can I connect it to this PCI-e Adapter Card,Compatible for SSD from MacBook Air(2013-2017) and MacBook PRO(Late 2013-2015) and then copy the data to my new 2016 Macbook pro?

https://desertcart.co.uk/products/9354316-sintech-...

If not, any ideas how I read/copy the data off the hard disk?